The FBI apparently believes that Etan Patz could still be alive — and reached out to a man just last month to chase down a tip that he might be theSoho child who vanished almost 35 years ago.

“Obviously, I was surprised,’’ the man told the Web site ProPublica of the e-mail he got from a federal agent, followed by a phone call, asking him questions about his past.

“I chuckled. I thought it was funny because it was so unlikely that it would be possible that I could be this person.

“I had no idea who Etan Patz was.”

But the agent was dead serious, suggesting to the unidentified American — who now works and lives with his wife in Europe — that he might not have been born where he’d been told and that the couple he considered his mom and dad weren’t actually his biological parents.

The agent explained that he was investigating an anonymous tip that the man could be Etan, who disappeared on his way to school in Soho on the morning of May 25, 1979.

“I thought it was a hoax,’’ the man told the investigative site, noting that he had to go to Wikipedia to find out about the case.

But the agent persisted, asking him questions such as where he’d lived and gone to school.

The man, who has been living abroad for two years, said it didn’t make any sense because, among other things, he was 30, or 11 years younger than Etan would have been this year.

The man, who is close to his family in the United States, said he asked the agent why he was still pursuing leads that the boy was alive, given that Pedro Hernandez, a former bodega worker, confessed in 2012 to killing the 6-year-old.

The agent didn’t respond, the man said.

FBI sources have already said they don’t believe that Hernandez is the killer. They say his confession — which he has since recanted — has too many inconsistencies, and he has a history of mental illness.

But sources with the NYPD and Manhattan DA’s Office, which is prosecuting Hernandez, insist that they have their man.

“It’s far-fetched and ridiculous’’ to think that Patz is still alive, a source close to the investigation told The Post on Monday.

Hernandez’s lawyer, Harvey Fishbein, declined to comment, and the FBI did not respond to a request for comment.

The next hearing in the case against Hernandez is set for Feb. 18, with the trial scheduled to start in April.

The man questioned by the agent contacted ProPublica after the site did an article on the controversy over Hernandez’s arrest.

“I thought you might want to know that the FBI may be working to prove the child is still alive,” the man told the Web site.